Video streaming performance may degrade substantially in a mobile environment due to fast-changing wireless links. On the other hand, to provide ubiquitous services, heterogeneous static and mobile access and backbone networks will be integrated in the sixth-generation (6G) systems, so mobile users can take advantage of multiple access options for better services. Multi-path transport-layer protocols like Multi-Path QUIC (MPQUIC) show promise in utilizing multiple access links to address the impact of mobility. However, the optimal link selection that aims to provide statistical QoS guarantee for video streaming in a mobile environment with both user mobility and network mobility remains an open issue. In this paper, based on a lightweight Multi-Armed Bandit (MAB) technique, we develop a Q oS-driven C ontextual MAB (QC-MAB) framework for MPQUIC, which makes an intelligent access network selection and adaptively enables FEC coding to trade off delay, reliability and goodput. Extensive simulation results with ns-3 show that the proposed QC-MAB framework can outperform the state-of-the-art solutions. It achieves up to ten times lower video interruption ratio and three times higher goodput in highly dynamic mobile environments.